Abstract

It would be useful to have a category of extensive-form games whose isomorphisms specify equivalences between games. Since working with entire games is too large a project for a single paper, I begin here with preforms, where a “preform” is a rooted tree together with choices and information sets. In particular, this paper first defines the category \, whose objects are “functioned trees”, which are specially designed to be incorporated into preforms. I show that \ is isomorphic to the full subcategory of \ whose objects are converging arborescences. Then the paper defines the category \, whose objects are “node-and-choice preforms”, each of which consists of a node set, a choice set, and an operator mapping node-choice pairs to nodes. I characterize the \ isomorphisms, define a forgetful functor from \ to \, and show that \ is equivalent to the full subcategory of \ whose objects are perfect-information preforms. The paper also shows that many game-theoretic entities can be derived from preforms, and that these entities are well-behaved with respect to \ morphisms and isomorphisms.